According to John S. Wilkins in his recent guest post over at Punctuated Equilibrium (also here on John's blog) there are either 26-27, 7, 2, 1 or 0. The article is well worth the read as John gives a nice, brief overview of the many different definitions of a biological species, their similarities and differences, and the key concepts behind those definitions.
If you don't mind my giving away the punchline, here's what it all boils down to:
For a more detailed treatment of the idea of biological species, see John's book 'Species: A History of the Idea'.
Final score: 26-27, 7, 2, 1 or 0.
What to think? My solution is this:
There is one species concept (and it refers to real species).
There are two explanations of why real species are species (see my microbial paper, 2007): ecological adaptation and reproductive reach.
There are seven distinct definitions of "species", and 27 variations and mixtures.
And there are n+1 definitions of "species" in a room of n biologists.
[Hat tip to John Hawks and GrrlScientist]